Shunt capacitance is neglected in the analysis of short transmission lines. This is because the shunt capacitance is relatively small in short lines as compared to its resistance and inductance. Therefore, it can be assumed that the line is purely resistive and inductive.

Explanation:
Shunt capacitance is the capacitance between the line conductors and the ground or between the conductors themselves. It is represented by a capacitor in the equivalent circuit of a transmission line. Shunt capacitance causes the current to flow from the line conductors to the ground or between conductors, resulting in a capacitive reactance. This reactance decreases the power-carrying capacity of the transmission line.

However, in the case of short transmission lines, the length of the line is small, usually less than 80 km. As a result, the shunt capacitance is small compared to the resistance and inductance of the line. Therefore, the capacitive reactance is negligible, and it can be assumed that the line is purely resistive and inductive.

In the analysis of long and medium transmission lines, the shunt capacitance cannot be neglected. In these cases, the length of the line is significant, resulting in a substantial shunt capacitance. Shunt capacitance causes a capacitive reactance, which significantly affects the line's performance, leading to voltage drop and power loss. Therefore, the shunt capacitance must be taken into account while analyzing long and medium transmission lines.

Conclusion:
Shunt capacitance is negligible in short transmission lines, and it can be assumed that the line is purely resistive and inductive. In contrast, shunt capacitance cannot be neglected in the analysis of long and medium transmission lines as it significantly affects the line's performance.